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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.07254 |
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Table of Contents:
- A total weighting of a graph $G$ is a mapping $ϕ$ that assigns a weight to each vertex and each edge of $G$. The vertex-sum of $v \in V(G)$ with respect to $ϕ$ is $S_ϕ(v)=\sum_{e\in E(v)}ϕ(e)+ϕ(v)$. A total weighting is proper if adjacent vertices have distinct vertex-sums. A graph $G=(V,E)$ is called $(k,k')$-choosable if the following is true: If each vertex $x$ is assigned a set $L(x)$ of $k$ real numbers, and each edge $e$ is assigned a set $L(e)$ of $k'$ real numbers, then there is a proper total weighting $ϕ$ with $ϕ(y)\in L(y)$ for any $y \in V \cup E$. In this paper, we prove that the generalized Petersen graphs are $(1,3)$-choosable.